The κ-Lattice : Decidability Boundaries for Qualitative Analysis in Biological Languages

The κ-calculus is a formalism for modelling molecular biology where molecules are terms with internal state and sites, bonds are represented by shared names labelling sites, and reactions are represented by rewriting rules. Depending on the shape of the rewriting rules, a lattice of dialects of κ can be obtained. We analyze the expressive power of some of these dialects by focusing on the thin boundary between decidability and undecidability for problems like reachability and coverability. This analysis may be used, for instance, for excluding the genesis of dangerous substances.

[1]  Wolfgang Reisig,et al.  Petri Nets , 1985, EATCS Monographs on Theoretical Computer Science.

[2]  P. Hsieh,et al.  The kinetics of spontaneous DNA branch migration. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[3]  R. Fraser.  The structure of deoxyribose nucleic acid. , 2004, Journal of structural biology.

[4]  Jean-Marc Talbot,et al.  When Ambients Cannot Be Opened , 2003, FoSSaCS.

[5]  Richard Mayr,et al.  Process rewrite systems , 1999, EXPRESS.

[6]  Gianluigi Zavattaro,et al.  Reachability Analysis in BioAmbients , 2008, MeCBIC.

[7]  Jin Yang,et al.  Graph Theory for Rule-Based Modeling of Biochemical Networks , 2006, Trans. Comp. Sys. Biology.

[8]  Luca Cardelli,et al.  Efficient, Correct Simulation of Biological Processes in the Stochastic Pi-calculus , 2007, CMSB.

[9]  François Fages,et al.  Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM , 2002 .

[10]  Kai Salomaa,et al.  Deterministic Tree Pushdown Automata and Monadic Tree Rewriting Systems , 1988, J. Comput. Syst. Sci..

[11]  Harry M. T. Choi,et al.  Programming biomolecular self-assembly pathways , 2008, Nature.

[12]  Luca Cardelli,et al.  On the Computational Power of Biochemistry , 2008, AB.

[13]  Sophie Tison,et al.  The theory of ground rewrite systems is decidable , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[14]  Barbara König,et al.  Applying the Graph Minor Theorem to the Verification of Graph Transformation Systems , 2008, CAV.

[15]  Annegret Habel,et al.  Hyperedge Replacement, Graph Grammars , 1997, Handbook of Graph Grammars.

[16]  Flemming Nielson,et al.  Pathway analysis for BioAmbients , 2008, J. Log. Algebraic Methods Program..

[17]  N. Seeman,et al.  Assembly of Borromean rings from DNA , 1997, Nature.

[18]  Sándor Vágvölgyi,et al.  Bottom-Up Tree Pushdown Automata and Rewrite Systems , 1991, RTA.

[19]  Carolyn L. Talcott,et al.  Pathway Logic , 2008, SFM.

[20]  Nadia Busi,et al.  Deciding Reachability in Mobile Ambients , 2005, ESOP.

[21]  Marvin Minsky,et al.  Computation : finite and infinite machines , 2016 .

[22]  M. Rusinowitch,et al.  Reachability is decidable for ground AC Rewrite systems , 1998 .

[23]  Giorgio Delzanno,et al.  On Reachability and Spatial Reachability in Fragments of BioAmbients , 2007, Electron. Notes Theor. Comput. Sci..

[24]  Mogens Nielsen,et al.  Decidability Issues for Petri Nets - a survey , 1994, Bull. EATCS.

[25]  Carolyn L. Talcott,et al.  The Pathalyzer: A Tool for Analysis of Signal Transduction Pathways , 2005, Systems Biology and Regulatory Genomics.

[26]  Monika Heiner,et al.  Petri Nets for Systems and Synthetic Biology , 2008, SFM.

[27]  Cosimo Laneve,et al.  Modelizations and Simulations of Nano Devices in nanok calculus , 2007 .

[28]  José Meseguer,et al.  Pathway Logic: Symbolic Analysis of Biological Signaling , 2001, Pacific Symposium on Biocomputing.

[29]  Florent Jacquemard,et al.  Decidable Approximations of Term Rewriting Systems , 1996, RTA.

[30]  Cosimo Laneve,et al.  Formal molecular biology , 2004, Theor. Comput. Sci..

[31]  Philippe Schnoebelen,et al.  Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[32]  Nadia Busi,et al.  Reachability Analysis in Boxed Ambients , 2005, ICTCS.

[33]  Luca Cardelli,et al.  Termination Problems in Chemical Kinetics , 2008, CONCUR.

[34]  Vincent Danos,et al.  Abstract Interpretation of Cellular Signalling Networks , 2008, VMCAI.

[35]  G. Whitesides,et al.  Molecular self-assembly and nanochemistry: a chemical strategy for the synthesis of nanostructures. , 1991, Science.

[36]  Cosimo Laneve,et al.  The kappa-Lattice: Decidability Boundaries for Qualitative Analysis in Biological Languages , 2009, CMSB.

[37]  François Fages,et al.  Formal Cell Biology in Biocham , 2008, SFM.

[38]  Russ B. Altman,et al.  Modelling biological processes using workflow and Petri Net models , 2002, Bioinform..